J. Eur. Opt. Society-Rapid Publ. 2026, 22, 19 Ó The Author( s), published by EDP Sciences, 2026 https:// doi. org / 10.1051 / jeos / 2026011 Available online at: https:// jeos. edpsciences. org
EOSAM 2025 Guest editors: Omar El Gawhary, Stefan Witte, Ignacio Moreno
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Propagation of partially coherent fields radiated by sources with univariable cross-spectral density
Massimo Santarsiero 1, Rosario Martínez-Herrero 2, Juan Carlos González de Sande 3 |
, Gemma Piquero 2,* |
, |
Olga Korotkova 4, and Franco Gori 1 |
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1 |
DIIEM, Università Roma Tre, via V. Volterra 62, Rome 00146, Italy |
2 |
Departamento de Óptica, Fac. CC. Físicas, U. C. M., Ciudad Universitaria s / n, 28040 Madrid, Spain |
3 |
Universidad Politécnica de Madrid, ETSIS de Telecomunicación, Campus Sur, 28031 Madrid, Spain |
4 |
Department of Physics, University of Miami, 1320 Campo Sano Drive, Coral Gables, FL, 33146, USA |
Received 18 December 2025 / Accepted 4 February 2026
Abstract. A new class of partially coherent light sources, the sources with uni-variable cross-spectral density( CSD), has been recently introduced. Their CSD is obtained starting from any function of a single complex argument having non-negative Taylor coefficients. This allows the conception of a virtually infinite number of physically realizable partially coherent sources. Here, the main characteristics of sources of this class are investigated through examples, with particular reference to the irradiance and coherence properties across the source plane and upon propagation, both in the near and in the far field. Furthermore, since the coherent modes of such sources present optical vortices, parameters quantifying the vortex structure of the field across the source plane are also evaluated for the presented cases.
Keywords: Coherence, Coherent modes, Propagation, Optical vortices, Orbital angular moment, Structured coherence.
1 Introduction
Structured light has attracted strong interest in recent years, largely driven by its wide range of applications and by rapid progress in generating and detecting tailored optical fields [ 1, 2 ]. Within this area, partially coherent sources are increasingly regarded not as a limitation but as a useful degree of freedom, since the engineering of spatial coherence can mitigate drawbacks of highly coherent beams. Recent reviews emphasize that partially coherent beams with structured coherence have been explored for concrete applications including: optical imaging [ 3, 4 ], free-space optical communications with improved robustness to atmospheric turbulence [ 5 – 8 ], coherence-based optical encryption and robust signal / information transmission through complex or scattering media [ 8, 9 ], optical manipulation [ 10, 11 ], and remote sensing [ 12 ]. These are some of the reasons why there is great interest in devising, realizing, and characterizing new light sources, both coherent and partially coherent, that allow the characteristics of the light radiated by these sources to be modified in a controlled way [ 13 – 38 ].
Interesting and promising results are derived from the presence of phase vortices, which confer unique capabilities
* Corresponding author: piquero @ ucm. es to the beam radiated from the source [ 5, 6, 12, 39 – 54 ]. For example, they find application in optical manipulation, because they can exert torque on microscopic particles, enabling advanced optical tweezers and micromanipulation [ 10, 46 ]; in imaging and metrology, where they offer new possibilities for super-resolution or phase-sensitive detection [ 12, 44 ]; in optical communication, since they provide an extra degree of freedom, the orbital angular momentum( OAM), for multiplexing and increasing data capacity [ 5, 6 ]. Vortex beams are typically generated using elements such as spiral phase plates, computer-generated holograms, q plates, or metasurfaces that encode the desired OAM mode [ 47, 50, 51, 53 ].
Recently, a new type of partially coherent light source, namely, a source with uni-variable cross-spectral density( CSD), has been proposed [ 38 ]. The peculiarity of sources of this class is that their CSD [ 55 ] can be directly derived from a function of a single complex variable [ 38 ]. The only requirement this function has to fulfill in order for it to be associated with a well-defined CSD is that its Taylor expansion must involve only non-negative coefficients. Several analytical forms, in some cases very simple, of bona-fide CSD can be devised in this way. Sources with uni-variable CSD are defined within a finite circular region, related to the convergence domain of the above Taylor series, and
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